To begin the exploration of what topics in number and operations look like in a classroom at your grade level, watch a video segment of a teacher who took the Number and Operations course and then adapted the mathematics to her own teaching situation.

In the video segment, Ms. Donnell introduces students to That's Logical! puzzles, which can be solved by using logic, spatial clues, and number theory clues. Each puzzle consists of a three-by-three grid and a set of clues to help students decide where to place the numbers 1 through 9 on the grid. When the numbers are placed correctly, all the clues are true. Read the information on clue grids and the clues below before watching the video segment.

The Clue Grids
Each clue grid consists of several cells from the puzzle grid. Each cell contains a symbol that tells you something about the digit in that cell. These clue grids may be put in the puzzle grid in any way they'll fit without turning or flipping. Some clues are fixed -- i.e., the clue grids can be fit onto the puzzle in only one way. Other clue grids can be fit onto the puzzle in a few different ways.

The Clues

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The letter E stands for an even number (2, 4, 6, or 8). An E with a slash through it means the number is not even.

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A square stands for a square number (1, 4, or 9). A square with a slash through it means the number is not square.

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A triangle stands for a triangular number (1, 3, or 6). A triangle with a slash through it means the number is not triangular.

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A cube stands for a cubic number (1 or 8). A cube with a slash through it means the number is not cubic.

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The letter P stands for a prime number (2, 3, 5, or 7). A P with a slash through it means the number is not prime.

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A number stands for itself. A number with a slash through it means any number but that number.

Before watching the video segment, you might like to try this sample puzzle and its solution. When viewing the video segment, keep the following questions in mind: Note 2

a.

What fundamental ideas (content) about number and operations is the teacher trying to teach?

b.

What mathematical processes does the teacher expect students to demonstrate?

c.

How do students demonstrate their knowledge of the intended content? What does the teacher do to elicit student thinking?

Video SegmentIn this segment, Ms. Donnell explains the That's Logical! puzzles and has students try to solve a puzzle with two fixed clues.

If you are using a VCR, you can find this segment on the session video approximately 6 minutes and 56 seconds after the Annenberg Media logo.

Problem A1

Answer questions (a), (b), and (c) above.

Problem A2

At what point(s) in the lesson are the students learning new content?

Problem A3

Discuss the role of manipulatives in Ms. Donnell's lesson. How do they help deepen the students' knowledge of the content area?

Problem A4

Ms. Donnell's lesson was based on Session 6 of this course. Discuss the ways in which her lesson was similar to and different from the one in this course. What adaptations did she make, and why?